Topologically Controlled Lossy Compression.

This paper presents a new algorithm for the lossy compression of scalar datadefined on 2D or 3D regular grids, with topological control. Certain techniquesallow users to control the pointwise error induced by the compression. However,in many scenarios it is desirable to control in a similar way the preservationof higher-level notions, such as topological features , in order to provideguarantees on the outcome of post-hoc data analyses. This paper presents thefirst compression technique for scalar data which supports a strictlycontrolled loss of topological features. It provides users with specificguarantees both on the preservation of the important features and on the sizeof the smaller features destroyed during compression. In particular, we presenta simple compression strategy based on a topologically adaptive quantization ofthe range. Our algorithm provides strong guarantees on the bottleneck distancebetween persistence diagrams of the input and decompressed data, specificallythose associated with extrema. A simple extension of our strategy additionallyenables a control on the pointwise error. We also show how to combine ourapproach with state-of-the-art compressors, to further improve the geometricalreconstruction. Extensive experiments, for comparable compression rates,demonstrate the superiority of our algorithm in terms of the preservation oftopological features. We show the utility of our approach by illustrating thecompatibility between the output of post-hoc topological data analysispipelines, executed on the input and decompressed data, for simulated oracquired data sets. We also provide a lightweight VTK-based C++ implementationof our approach for reproduction purposes.